Finite-Amplitude, Shockless, Resonant Vibrations of an Inhomogeneous Elastic Panel

Abstract

An inhomogeneous, nonlinear elastic panel, fixed at one end, is subject to a resonant harmonic forcing at the other. The vibrations in an equivalent homogeneous panel would contain shocks. We exhibit a class of finite inhomogeneities that produces a panel response that is harmonic but does not contain shocks. The finite-strength inhomogeneity is capable of inhibiting the nonlinear distortion sufficiently to prevent shocks from forming. This is not the case for a “slow” inhomogeneity that can be described using a geometrical acoustics approximation.